A) The answer is 11.53 m/s
The final kinetic energy (KEf) is the sum of initial kinetic energy (KEi) and initial potential energy (PEi).
KEf = KEi + PEi
Kinetic energy depends on mass (m) and velocity (v)
KEf = 1/2 m * vf²
KEi = 1/2 m * vi²
Potential energy depends on mass (m), acceleration (a), and height (h):
PEi = m * a * h
So:
KEf = KEi + <span>PEi
</span>1/2 m * vf² = 1/2 m * vi² + m * a * h
..
Divide all sides by m:
1/2 vf² = 1/2 vi² + a * h
We know:
vi = 9.87 m/s
a = 9.8 m/s²
h = 1.81 m
1/2 vf² = 1/2 * 9.87² + 9.8 * 1.81
1/2 vf² = 48.71 + 17.74
1/2 vf² = 66.45
vf² = 66.45 * 2
vf² = 132.9
vf = √132.9
vf = 11.53 m/s
b) The answer is 6.78 m
The kinetic energy at the bottom (KE) is equal to the potential energy at the highest point (PE)
KE = PE
Kinetic energy depends on mass (m) and velocity (v)
KE = 1/2 m * v²
Potential energy depends on mass (m), acceleration (a), and height (h):
PE = m * a * h
KE = PE
1/2 m * v² = m * a * h
Divide both sides by m:
1/2 * v² = a * h
v = 11.53 m/s
a = 9.8 m/s²
h = ?
1/2 * 11.53² = 9.8 * h
1/2 * 132.94 = 9.8 * h
66.47 = 9.8 * h
h = 66.47 / 9.8
h = 6.78 m
Answer:
Option C) 2,090 J/(mol K)
Explanation:
Data:
Volume in the beaker = 429 ml
temperature = 20° C
Density = 789 kg/m³
Equilibrium reading = 429
volume change = 29 ml
= 0.029 L
Energy change = mcΔT
U + PΔV
Answer:
Part(a): The frequency is
.
Part(b): The speed of the wave is
.
Explanation:
Given:
The distance between the crests of the wave,
.
The time required for the wave to laps against the pier, 
The distance between any two crests of a wave is known as the wavelength of the wave. So the wavelength of the wave is
.
Also, the time required for the wave for each laps is the time period of oscillation and it is given by
.
Part(a):
The relation between the frequency and time period is given by

Substituting the value of
in equation (1), we have

Part(b):
The relation between the velocity of a wave to its frequency is given by

Substituting the value of
and
in equation (2), we have

(1) Doubling of the current through the wire will result in doubling of its magnetic field.
The magnetic field around a wire is a function of the current I and radial distance r

(with mu denoting the magnetic permeability of the medium). So, B is directly proportional to I. The field magnitude will double with the doubled current from 5A to 10A
(2) Using the same formula as in (1), we can see that the magnetic field is inversely proportional to the radial distance from the wire. So, a particle at 20cm will experience half the magnitude compared to a particle at 10cm.
(3) Answer
If a particle with a charge q moves through a magnetic field B with velocity v, it will be acted on by the magnetic force

So, a particle with charge -2uC will experience a magnetic force of same magnitude but opposite direction (and perpendicular to B) as compared to a particle with a charge of 2uC
Answer:
Vf= 3.435 m/s
Explanation:
Given:
Initial velocity Vi =0 m/s (starting from Rest position)
θ = 37⁰
Distance S = 1 m
To find: Final Velocity Vf=?
fist we have to find the down slope net acceleration a = g sin θ
a= 9.81 sin 37⁰ = 5.9 m/s²
By 3rd equation of motion
2 a S= Vf² - Vi²
Vf = Square root ( 2 × 5.9 m/s² × 1 + 0 m/s)
Vf = Square root (11.8)
Vf= 3.435 m/s